Convergent Point Motion Alignment
Compare a measured tangent-plane proper-motion direction with the great-circle direction to a supplied cluster apex; alignment does not establish membership.
Description
A convergent-point screen compares a star's proper-motion direction with the great-circle bearing toward a supplied cluster apex.
A convergent-point screen compares a star's proper-motion direction with the great-circle bearing toward a supplied cluster apex. Direction alignment is evidence to inspect, not a membership probability.1
Compare a measured tangent-plane proper-motion direction with the great-circle direction to a supplied cluster apex; alignment does not establish membership.
When to use Convergent Point Motion Alignment
Use this tool to compare a measured tangent-plane proper-motion direction with the great-circle direction to a supplied cluster apex; alignment does not establish membership.
Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
How to use Convergent Point Motion Alignment and understand its results
- Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
- Enter starRaDegrees, starDecDegrees, apexRaDegrees, apexDecDegrees, eastProperMotion, northProperMotion, maximumMisalignmentDegrees using the field table and calculation rules, then run the tool.
- Read apexPositionAngleDegrees, motionMisalignmentDegrees, alignedWithApex. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| starRaDegrees | Star ra degrees | number | Required |
| starDecDegrees | Star dec degrees | number | Required |
| apexRaDegrees | Apex ra degrees | number | Required |
| apexDecDegrees | Apex dec degrees | number | Required |
| eastProperMotion | East proper motion | number | Required |
| northProperMotion | North proper motion | number | Required |
| maximumMisalignmentDegrees | Maximum misalignment degrees | number | Required |
Enter star/apex RA and Dec degrees, nonzero east/north proper motion and degree tolerance 0–180. The tool derives the tangent bearing to the apex and motion angle east of north, then compares their shortest angular difference inclusively. A zero apex tangent direction or zero measured motion is an input error.
misalignment=|shortestAngle(motionPositionAngle−apexPositionAngle)| Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| apexPositionAngleDegrees | Apex position angle degrees | number |
| motionMisalignmentDegrees | Motion misalignment degrees | number |
| alignedWithApex | Aligned with apex | boolean |
{
"input": {
"starRaDegrees": 0,
"starDecDegrees": 0,
"apexRaDegrees": 90,
"apexDecDegrees": 0,
"eastProperMotion": 1,
"northProperMotion": 0,
"maximumMisalignmentDegrees": 5
},
"output": {
"apexPositionAngleDegrees": 90,
"motionMisalignmentDegrees": 0,
"alignedWithApex": true
}
}Limitations and assumptions
It does not determine the apex, account for uncertainties or assess distance and radial velocity. Coincident/antipodal geometry has undefined bearing and extremely near cases may be numerically sensitive.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Moving Cluster Distance: Solve a moving-cluster distance from radial velocity and proper motion toward the convergent point; coherent bulk motion and negligible expansion are assumed. For a complementary task, use Common Motion Covariance Screen: Screen common proper motion with a supplied combined two-coordinate covariance; the relative Gaussian likelihood is not a membership probability or prior.
References
-
Convergent Point Motion Alignment — tool.io
Similar or alternative tools
- Moving Cluster Distance
Solve a moving-cluster distance from radial velocity and proper motion toward the convergent point; coherent bulk motion and negligible expansion are assumed.
- Common Motion Covariance Screen
Screen common proper motion with a supplied combined two-coordinate covariance; the relative Gaussian likelihood is not a membership probability or prior.